How would I multiply these two exponents?

Alice plans to buy a house. She has $2,000 in her savings account.

She plans to contribute $150 to the account each month.

We know that with each month, n, she deposits $150 and so, each month, her savings account balance increases by $150.

This simply means that after n months, her savings account balance would have increased by:

150 * n = 150n

Her initial balance was $2000, therefore, her balance after n months will be the sum of 150n and the amount that was initially there.

That is:

f(n) = 2000 + 150n

This is the function that describes the relationship between the number of months and her balance.

The solution for the given inequality is −8<x<3 or 3<x<7.

The given inequality is (x+8)(x-3)²(x-7)³<0.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality can be solved as follows

Solve for x by simplifying both sides of the inequality, then isolating the variable.

Inequality Form: x+8<0

x<-8 (Subtract 8 on both the sides of the inequality)

(x-3)²<0

⇒ x-3<0

⇒ x<3 (Add 3 on both the sides of the inequality)

(x-7)³<0

⇒ x-7<0

⇒ x<7 (Add 7 on both the sides of the inequality)

Solution is −8<x<3 or 3<x<7

Therefore, the solution for the given inequality is −8<x<3 or 3<x<7.

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After thoroughly calculation, we have come to find that, If equation x² = 25, where x ε z then x = √25 = 5, thus x is 5.

Equation, also known as a statement of equality between two expressions with variable- and/or number-based components. Since equations are essentially questions, efforts to systematically find answers to those questions have been the driving force behind the development of mathematics.

From straightforward algebraic equations that only require addition or multiplication to differential equations, exponential equations that use exponential expressions, and integral equations, there are many different types of equations that range in complexity. Numerous physics laws are expressed using them.

Simultaneously occurring equations, or system of equations Algebra requires the simultaneous solution of two or more equations (i.e., the solution must satisfy all the equations in the system). The quantity of equations must match the quantity of unknowns for a system to have a distinct solution.

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Okay, here we have this:

Considering the provided set of numbers we are going to organize the numbers from smallest to largest, so we obtain the following:

Remember that 5/6 is approximately 0.83 and 4/5 is 0.8, then:

Considering the number line and that the smaller numbers are further to the left and the larger numbers are further to the right, we are left with the following order from least to greatest: 4/5, 0.82, 5/6.

The equation for the situation a company prints designs on T-shirts is (40+12x) when x is the number of T-shirts.

According to the situation,

We have the following information:

The company charges $40 for set-up costs plus $12 per shirt.

So, the basic charge is added to every t-shirt.

Now, let's take the number of T-shirts on which the company prints designs on shirts to be x.

So, we have the charge for x number of t-shirts is:

$(40+12x)

Hence, the equation for the situation a company prints designs on T-shirts is (40+12x) when x is the number of T-shirts.

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Let

A

be the event of selecting an American that believes that some people see the future in their dreams. From the problem,

P(A)=62.4%=0.624

Let

A' be the event of selecting an American who does not believe that some people see the future in their dreams

Remember that

P(A')=1-P(A)

substitute given value

P(A')=1-0.624=0.376=37.6%

Hence, the probability of randomly selecting someone who does not believe that some people see the future in their dreams is 37.6%

The fraction of fishes which are guppies in Marcus's aquarium is 2/3

Number of gold fishes in the aquarium = 1/9

Number of angelfish in the aquarium = 5/9

Fractions: A numerical value that designates a portion of a whole is used to represent fractions. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

Let x be the total number of fishes in Marcus's aquarium:

Number of guppies = Total fishes - Number of gold fishes - Number of angelfishes

= x - 1/9 - 5/9

= x - 6/9

x = 6/9 or 2/3

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The equation of the line 3y + x = 3 through pair of points (0,1) and (3,0), the equation of the line 6y = 2x +3 through pair of points (1/2,2/3) and (-3/2,5/3) and the equation of the line  y = 2x + 4 through pair of points (-3,-2) and (1,6)

The equation of the line through pair of points (0,1) and (3,0)

⇒ y - y₁ = [(y₂ - y₁)/(x₂ -x₁ )](x - x₁ )

Here x₁ = 0 and y₁ = 1

x₂ = 3 and y₂ = 0

The equation of the line is obtained by substituting these values into the above equation;

⇒ y - 1 = [(0-1)/(3-0)](x -0)

⇒ y - 1 = (-1/3)x

⇒ 3y - 3 = x

⇒ 3y + x = 3

The equation of the line through pair of points (1/2,2/3) and (-3/2,5/3)

⇒ y - 2/3 = [(5/3 -2/3)/(-3/2-1/2)](x -1/2)

⇒ y - 2/3 = [(3/3)/(-4/2)](x -1/2)

⇒ y - 2/3 = (1/3)(x -1/2)

Multiply by 6 both sides of the equation,

⇒ 6y - 4 = 2(x -1/2)

⇒ 6y = 2x -1 + 4

⇒ 6y = 2x +3

The equation of the line through pair of points (-3,-2) and (1,6)

⇒ y - (-2) = [(6-(-2))/(1-(-3))](x -(-3))

⇒ y + 2= (8/4)(x + 3)

⇒ y = 2x + 6 -2

⇒ y = 2x + 4

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The table of values to represent the relationship between the number of days and the number of puzzles she has completed will be:

Days Puzzle completed

1. 4

2. 8

3. 12

4. 16

5. 20

From the information, Maddie is determind to finish some extra credit math homework by completeing 4 math puzzles each day.

Therefore, the first day, she will do 4 puzzles. The second day will be:

= 2 × 4 = 8 puzzles

Third day = 3 × 4 = 12 puzzles.

In this case, the method that was used is simply to multiply the number of days by 4 since he does 4 puzzles everyday.

It should be noted that this illustrates a proportional relationship

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24x +8y ≥ 20

3x - 6y > 24

First, express both equations in slope-intercept form

y= mx+b

Where:

m= slope ( rise (y) / run (x))

b= y-intercept (where the line crosses the y axis)

Solve for y:

24x +8y ≥ 20

8y ≥ -24x +20

y ≥ (-24x +20 ) / 8

y ≥ -3x + 2.5

3x - 6y > 24

-6y > 24- 3x

y < (24 -3x) / -6

y < 1/2x -4

System:

y ≥ -3x + 2.5

y < 1/2x -4

Solution = the area where the 2 solutions overlap (blue+ red)

Question:

Solve

4n + 1 = 25

Solution:

Consider the following formula:

this is equivalent to:

this is equivalent to:

solving for n, we get

Then, we can conclude that the correct answer is:

Given:

a) The radius is​ doubled.

b) The radius is​ tripled.

To find:

The changes to the surface area of a sphere

Explanation:

Let us take the original radius as r.

The surface area of the original sphere is,

a) The new radius will be,

So, the surface area of the sphere with the new radius is,

Therefore, the surface area of a sphere becomes four times the original surface area if the radius is​ doubled.

b) The new radius will be,

So, the surface area of the sphere with the new radius is,

Therefore, the surface area of a sphere becomes nine times the original surface area if the radius is​ tripled.

The coordinates of the other endpoint  of the segment, given its midpoint and one endpoint are (-14, -9)

The Midpoint Formula for a line with endpoints as (x₁, y₁) and (x₂, y₂) is;

((x₁ + x₂)/2, (y₁ + y₂)/2)

We are given the  following;

Midpoint (-15,-6)

End point (-16,-3)

Let x₁ = -16, the x coordinate of the endpoint

Let x₂ = the x coordinate of the unknown endpoint

Let y₁ = -3, the y coordinate of the endpoint

Let y₂ = the y coordinate of the unknown endpoint

Thus, for the x coordinate of the unknown endpoint;

(x1 + x2)/2

(-16 + x₂)/2 = -15

-16 + x₂ = -30

x₂ = -14

For the y coordinate of the unknown endpoint;

(y1 + y2)/2

(-3 + y₂)/2 = -6

-3 + y₂ = -12

y₂ = -12 + 3

y₂ = -9

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The answer would be B.

The relationship is proportional. The constant of proportionality is 5.

Compute the given function

[tex]f(x)=- 3x^{2}-7x-3[/tex]

How the given function is computed?

Let us consider f (-3)

f(-3)= -3(9)- 7(-3) -3

     =-27+21-3

     = -9

Let us consider f (4)

f(4) = -3(16)-7(4)-3

    =-48-28-3

    = - 79

A) f(-3) * f (4)

= (-9) * (-79)

= 711

B) f(-3)  / f (4)

=  (-9) / (-79)

= 9/79 (or 0.11)

What are functions?

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The standard form of the quadratic function with vertex (-1,8) and passing through point (0,2) is y = -6(x+1)²+8.

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.

The standard form of a quadratic equation in vertex form is given as,

y = a(x-h)² + 8

Where (h,k) is the coordinate of the vertex and a is constant.

Given the vertex  (h,k) = (-1,8)

Substitute, vertex, and  (0,2)

2 = a(0 + 1)² + 8

a = -6

Therefore, the equation converts as,

y = -6(x+1)²+8

Hence "The standard form of the quadratic function with vertex (-1,8) and passing through point (0,2) is y = -6(x+1)²+8".

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Answer:

Step-by-step explanation:

The difference between two consecutive even integers is 2.

Let the first of the three integers is x, then the following ones are:

x + 2 and x + 4.

The sum of the three is - 78. Express it as equation and solve for x:

The integers are - 28, - 26 and - 24

The probability that you, Shirley, and Matthew are chosen is 0.0001

Probability:

Probability refers the measure of the likelihood of an event to occur.

The formula of Probability is

Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes

Given,

Suppose that your boss must choose three employees in your office to attend a conference in Jamaica. Because all 28 of you want to go, he decides that the only fair way is to draw names out of a hat.

Here we need to find the probability that you, Shirley, and Matthew are chosen.

Here we have assuming that the selection process is fair;

We know that, the total number of employees is 28

Therefore, the probability of selecting each employee is,

=> 1/28

So, the probability of selecting yourself, Shirley, and Matthew is calculated as,

=> 1/28 x 1/27 x 1/26

=> 1/19656

=> 0.00005

When we round off it into four decimal place then we get,

=> 0.0001

Therefore, the probability that you, Shirley, and Matthew are chosen 0.0001.

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Answer:

melissa spent approximately $491 in total

Considering the given linear function, it is found that:

a)

b) The discrete domain of the function is: {0, 1, 2, 3, 4, 5, 6, 7}.

c) The graph of the function is given at the end of the answer.

A linear function, in slope-intercept format, is modeled according to the rule given below:

y = mx + b

In which:

The amount of money you have remaining after printing p photographs is  modeled by the following function:

M(p) = 10 - 1.44p.

Hence the coefficients are as follows:

The number of photos printed is a discrete number, as this number cannot assume decimal values, hence the domain is also discrete.

You cannot print a negative value of numbers, neither can M(p) be negative, hence the domain, which is the number of photos you can print, is:

{0, 1, 2, 3, 4, 5, 6, 7}.

Considering the above domain, the graph of the function is given by the image at the end of the answer.

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Answer:

78.59$

Step-by-step explanation:

A lowest denominator to solve the given equation is 10.

What are fractions?

Fraction are ratios in which numerator and denominator are both integers and denominator is not zero.

We are given a equation

[tex]\frac{74}{5}+1\frac{9}{10}[/tex]

Upon solving we get the following

[tex]\frac{74}{5}+\frac{19}{10}[/tex]

If we multiply both numerator and denominator of the first term by 2 we get

[tex]\frac{148}{10}+\frac{19}{10}[/tex]

Hence after this we can add

Hence A lowest denominator to solve the given equation is 10

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According to the converse of corresponding angles theorem, the statement that allows Carmen to conclude that lines p and q are parallel is: ∠2 ≅ ∠6.

A transversal is a line that crosses two straight lines. For example, line t is a transversal that crosses the lines p and q in the given diagram above.

Parallel lines are lines that do not meet each other at any point and are of equal distant to each other.

When a transversal intersects two parallel lines, they form angle pairs. One of such angle pairs is, corresponding angles, which are always congruent to each other.

Thus, if corresponding angles are formed and are equal to each other, then the lines they lie on must be parallel lines based on the corresponding angles converse theorem.

Angles 2 and 6 are corresponding angles that are formed by the transversal that intersects lines q and p. If they are congruent angles, then the lines are parallel.

Therefore, Carmen can use the statement, ∠2 ≅ ∠6 to show that lines q and p are parallel.

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The solution of equation as ordered pairs can be given as {0, 3/2, 3, 6, 15/2}.

Domain may be defined as the input variable x for any of the given function which gives a suitable set of output variables y. The input variable is called the independent variable whereas the output variable is called the dependent variable. The equation given in the question 3x - 2y = -6 can also be expressed as y = (3x + 6)/2. The ordered pairs of Domain are {-2, -1, 0, 2, 3}. Now if we put these values as values of x we get the values of y as,

At x = -2, y = 0, at x = -1, y = 3/2, at x = 0, y = 3, at x = 2, y = 6 and at x = 3, y = 15/2.

These are the values of outputs, and the ordered pair will be expressed as

{0, 3/2, 3, 6, 15/2}.

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Answer:

5

Step-by-step explanation:

We know that - (-7) = +7, so

-2 - (-7) = -2 + 7 = 5

Problem

Steve scores in a card game is five points away from zero zinnias score is the opposite of an of Steve's score positive value what is the score ​

Solution

Let x the score for Steve and y the score for Denia.

We know that the score of Denia is the opposite of Steve

So then the scores needs to be:

Steve =-5

Denia =5

And with this we satisfy all the requirements

Answer: Correct! The answer is 12.

Step-by-step explanation:

1) Draw the triangle.

Drawing a triangle usually helps you see the problem better!
|    \

|        \  13 cm

|           \

|______\

  5 cm

2) Solve the other leg

To find the other leg, we need to use the Pythagorean theorem. Which goes like this

[tex]a^2+b^2=c^2[/tex]

We will then substitute the numbers into the equation

[tex]5^2+b^2=13^2[/tex]

Simplify

[tex]25+b^2=169[/tex]

Set the variable on one side

[tex]b^2=144[/tex]

Get rid of the squared in the b by square rooting both sides.

[tex]b=12[/tex]

The answer is 12.

Answer:

the 8 pack

Step-by-step explanation:

So to start we should find how much an individual capsule in each is

Well start off by 5.99/8 which will give us 0.74875 per capsule and well round in to 0.75 each to put it in terms of money.

Now we will do 2.85/2 which then gives you 1.425 and well say that's about 1.43 per capsule

Answer:

C

Step-by-step explanation:

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